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- W2786351418 abstract "The set of idempotents of any semigroup carries the structure of a biordered set, which contains a great deal of information concerning the idempotent generated subsemigroup of the semigroup in question. This leads to the construction of a free idempotent generated semigroup $mathsf{IG}(mathcal{E})$ - the `free-est' semigroup with a given biordered set $mathcal{E}$ of idempotents. We show that when $mathcal{E}$ is finite, the word problem for $mathsf{IG}(mathcal{E})$ is equivalent to a family of constraint satisfaction problems involving rational subsets of direct products of pairs of maximal subgroups of $mathsf{IG}(mathcal{E})$. As an application, we obtain decidability of the word problem for an important class of examples. Also, we prove that for finite $mathcal{E}$, $mathsf{IG}(mathcal{E})$ is always a weakly abundant semigroup satisfying the congruence condition." @default.
- W2786351418 created "2018-02-23" @default.
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- W2786351418 date "2018-02-07" @default.
- W2786351418 modified "2023-09-25" @default.
- W2786351418 title "A group-theoretical interpretation of the word problem for free idempotent generated semigroups" @default.
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- W2786351418 doi "https://doi.org/10.48550/arxiv.1802.02420" @default.
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